Number Pyramid — Definition, Formula & Examples
A number pyramid is a triangular arrangement of numbers where each block is calculated from the two blocks directly beneath it, usually by adding them together.
A number pyramid (also called an addition pyramid or brick wall puzzle) is a structured array of cells arranged in rows of decreasing size, where the value in each cell equals the sum of the two adjacent cells in the row immediately below it.
How It Works
Start with a bottom row of numbers. To fill the block above any two side-by-side numbers, add those two numbers together. Repeat this process row by row until you reach the single block at the top. Sometimes the pyramid gives you the top number and asks you to work backward to find missing values in lower rows, which involves subtraction.
Worked Example
Problem: Complete the number pyramid with bottom row: 2, 5, 3, 1.
Row 1 (bottom): Write the given numbers.
Row 2: Add each pair of neighbors from the bottom row.
Row 3: Add each pair of neighbors from Row 2.
Row 4 (top): Add the two values from Row 3.
Answer: The completed pyramid, from bottom to top: [2, 5, 3, 1], [7, 8, 4], [15, 12], [27].
Why It Matters
Number pyramids build fluency with addition and subtraction in a puzzle-like format. They also introduce early algebraic thinking — when a value is missing in the middle of the pyramid, students must reason backward using differences to find it.
Common Mistakes
Mistake: Adding blocks that are not directly next to each other (e.g., skipping a block).
Correction: Each block is the sum of only the two blocks that sit directly below it and touch it. Always use adjacent pairs.